4 ms·

Which begs the question… why are GPUs good at matrix multiplication?

by blowski 3y ago

NikkiA 3y ago
Because 3d graphics are mostly matrix multiplications.
- vorticalbox 3y ago
  This is like saying "cars are fast because cars are good at going fast"
  - blowski 3y ago
    I guess it's like "cars are fast because they use similar engines to motorbikes, which also go fast". Technically correct, but doesn't really provide any useful information we can learn from.
  - flohofwoe 3y ago
    GPUs haven't been developed in a vacuum, they were mostly created to accelerate rendering for 3D games, and 3D rendering is mostly about vector operations in up to 4 dimensions (to process points and vectors in 3D space, and pixels in an RGB+transparency 'color space'). The other interesting property of 3D rendering is that it is an 'embarrassingly parallel' problem. Vertices or pixels (mostly) don't depend on each other, so the GPU can process them in parallel. That's how GPUs turned over time into big arrays of very simple cores which are good at running a huge number of vector operations in parallel.
throwawaymaths 3y ago
They're actually kind of not, but they're good at vector multiplication. Matrix multiplication is just stacked vector multiplication, so GPUs are okay at matrix multiplication (but not as good as one could imagine they could be). I think TPUs were the first thing really designed to do matrix multiplication
dragontamer 3y ago
Because matrix multiplication parallelizes easily. 1. Matrix Multiplication caches easily: you can program the data-fetches to occur in blocks and recycle your memory-fetches across a huge number of operations. 2. Matrix Multiplication is innately parallel, with every square of the output matrix possibly computed in parallel. ----------- That being said: GPUs are not the best at this. Systolic processors are the best matrix multipliers and that's where NVidia Tensor Cores and/or Google TPUs come in. ------------ GPU / SIMD architecture was chosen for GPUs because video games have a large number of 4x4 matrix multiplications per frame. Every single vertex, of which a typical video game could have ~100 million vertexes, needs to be 4x4 matrix multiplied to determine where on the screen it has moved. GPUs need to perform this operation at 60 FPS for video gamers to be pleased, though some video gamers demand 120 FPS or even 200+ FPS. 4x4 is the operation of an affine transformation in 3d space (translation, rotation, scaling, etc. etc.). Most commonly for 'camera movement'. (Player moved to the right 5 ticks and then looked to the north-west by 27 degrees, where should all the objects in the screen move to? This is solved by matrix-multiplying all 100-million verticies with the camera-position matrix) 4x4 Matrix Multiplication isn't quite big enough to "deserve" a systolic processor yet.

Which begs the question… why are GPUs good at matrix multiplication?

NikkiA 3y ago

Because 3d graphics are mostly matrix multiplications.

vorticalbox 3y ago
This is like saying "cars are fast because cars are good at going fast"
- blowski 3y ago
  I guess it's like "cars are fast because they use similar engines to motorbikes, which also go fast". Technically correct, but doesn't really provide any useful information we can learn from.
- flohofwoe 3y ago
  GPUs haven't been developed in a vacuum, they were mostly created to accelerate rendering for 3D games, and 3D rendering is mostly about vector operations in up to 4 dimensions (to process points and vectors in 3D space, and pixels in an RGB+transparency 'color space'). The other interesting property of 3D rendering is that it is an 'embarrassingly parallel' problem. Vertices or pixels (mostly) don't depend on each other, so the GPU can process them in parallel. That's how GPUs turned over time into big arrays of very simple cores which are good at running a huge number of vector operations in parallel.

throwawaymaths 3y ago

They're actually kind of not, but they're good at vector multiplication. Matrix multiplication is just stacked vector multiplication, so GPUs are okay at matrix multiplication (but not as good as one could imagine they could be). I think TPUs were the first thing really designed to do matrix multiplication

dragontamer 3y ago

Because matrix multiplication parallelizes easily. 1. Matrix Multiplication caches easily: you can program the data-fetches to occur in blocks and recycle your memory-fetches across a huge number of operations. 2. Matrix Multiplication is innately parallel, with every square of the output matrix possibly computed in parallel. ----------- That being said: GPUs are not the best at this. Systolic processors are the best matrix multipliers and that's where NVidia Tensor Cores and/or Google TPUs come in. ------------ GPU / SIMD architecture was chosen for GPUs because video games have a large number of 4x4 matrix multiplications per frame. Every single vertex, of which a typical video game could have ~100 million vertexes, needs to be 4x4 matrix multiplied to determine where on the screen it has moved. GPUs need to perform this operation at 60 FPS for video gamers to be pleased, though some video gamers demand 120 FPS or even 200+ FPS. 4x4 is the operation of an affine transformation in 3d space (translation, rotation, scaling, etc. etc.). Most commonly for 'camera movement'. (Player moved to the right 5 ticks and then looked to the north-west by 27 degrees, where should all the objects in the screen move to? This is solved by matrix-multiplying all 100-million verticies with the camera-position matrix) 4x4 Matrix Multiplication isn't quite big enough to "deserve" a systolic processor yet.